{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,16]],"date-time":"2023-09-16T09:41:10Z","timestamp":1694857270362},"reference-count":10,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T00:00:00Z","timestamp":1541980800000},"content-version":"vor","delay-in-days":11,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["140 186412"],"award-info":[{"award-number":["140 186412"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we prove some cases of the gap\u20102 cardinal transfer theorem for uncountable languages assuming the axiom of constructibility. Consider uncountable cardinals <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0001\" \/>, with \u03bb regular, a first order language <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0002\" \/> with at least one unary predicate symbol <jats:italic>U<\/jats:italic>, with <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0003\" \/>. Given an <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0004.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0004\" \/>\u2010structure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0005.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0005\" \/>, where <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0006.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0006\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0007.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0007\" \/>, we find an <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0008.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0008\" \/>\u2010structure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0009.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0009\" \/> such that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0010.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0010\" \/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0011.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0011\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400079-math-0012.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400079:malq201400079-math-0012\" \/>.<\/jats:p>","DOI":"10.1002\/malq.201400079","type":"journal-article","created":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T13:20:01Z","timestamp":1542028801000},"page":"262-285","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The gap\u2010two cardinal problem for uncountable languages"],"prefix":"10.1002","volume":"64","author":[{"given":"Luis Miguel","family":"Villegas Silva","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas Universidad Aut\u00f3noma Metropolitana Iztapalapa Av. San Rafael Atlixco 186, Col. Vicentina Iztapalapa 09340 D.F. M\u00e9xico"},{"name":"Abteilung f\u00fcr Mathematische Logik Albert\u2010Ludwigs\u2010Universit\u00e4t Freiburg Ernst\u2010Zermelo\u2010Stra\u00dfe 1 79104 Freiburg Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,12]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Model\u2010Theoretic Logics, Perspectives in Mathematical Logic","author":"Barwise J.","year":"1985"},{"key":"e_1_2_8_3_1","volume-title":"Model Theory, third edition, Studies in Logic and the Foundations of Mathematics","author":"Chang C. C.","year":"1993"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059290"},{"key":"e_1_2_8_5_1","volume-title":"Constructibility, Perspectives in Mathematical Logic","author":"Devlin K.","year":"1984"},{"key":"e_1_2_8_6_1","volume-title":"A Shorter Model Theory","author":"Hodges W.","year":"1997"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0281602"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"e_1_2_8_9_1","unstructured":"R. B.Jensen Remarks on the two cardinal problem unpublished handwritten manuscript available online."},{"key":"e_1_2_8_10_1","unstructured":"A.Villaveces N.andL. M.Villegas S. Hanf numbers and two cardinal problems in infinitary logic in preparation."},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_11"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201400079","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T20:46:29Z","timestamp":1694810789000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201400079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11]]},"references-count":10,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1002\/malq.201400079"],"URL":"https:\/\/doi.org\/10.1002\/malq.201400079","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11]]},"assertion":[{"value":"2014-09-07","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-09-04","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}